A&A 542, A78 (2012) Astronomy DOI: 10.1051/0004-6361/201219134 & c ESO 2012 Astrophysics

Unique sextuple system: 65 Ursae Majoris

P. Zasche1,R.Uhlárˇ2, M. Šlechta3,M.Wolf1,P.Harmanec1,J.A.Nemravová1,andD.Korcákovᡠ1

1 Astronomical Institute, Faculty of Mathematics and Physics, Charles University Prague, 180 00 Praha 8, V Holešovickáchˇ 2, Czech Republic e-mail: [email protected] 2 Private Observatory, Pohoríˇ 71, 25401 Jílové u Prahy, Czech Republic 3 Astronomical Institute, Academy of Sciences, Fricovaˇ 298, 251 65 Ondrejov,ˇ Czech Republic Received 29 February 2012 / Accepted 28 March 2012

ABSTRACT

Context. The study of stellar multiple systems provides us with important information about the stellar formation processes and can help us to estimate the multiplicity fraction in the Galaxy. 65 UMa belongs to a rather small group of stellar systems of higher multiplicity, whose inner and outer are well-known. This allows us to study the long-term stability and evolution of the orbits in these systems. Aims. We obtained new photometric and spectroscopic data that when combined with interferometric data enables us to analyze the system 65 UMa and determine its basic physical properties. Methods. We perform a combined analysis of the light and curves, as well as the period variation by studying the times of the minima and the interferometric . A disentangling technique is used to perform the spectra decomposition. This combined approach allows us to study the long-term period changes in the system for the first time, identifying the period variation due to the motion on the visual orbit, in addition to some short-term modulation. Results. We find that the system contains one more component, hence we tread it as a sextuple hierarchical system. The most inner pair of components consists of an eclipsing binary orbiting around a barycenter on a circular orbit, both components being almost identical of spectral type about A7. This pair orbits on an eccentric orbit around a barycenter, and the third component orbits with a period of about 640 days. This motion is reflected in the period variation in the minima times of the eclipsing pair, as well as in the radial velocities of the primary, secondary, and tertiary components. Moreover, this system orbits around a barycenter with the distant component resolved interferometrically, whose period is of about 118 . Two more distant components (4 and 63)are also probably gravitationally bound to the system. The nodal period of the eclipsing-pair orbit is on the order of only a few centuries, which makes this system even more interesting for a future prospective detection of changing the depths of minima. Conclusions. We identify a unique solution of the system 65 UMa, decomposing the individual components and even shifting the system to higher multiplicity. The study of this kind of multiple can help us to understand the origin of stellar systems. Besides 65 UMa, only another 11 sextuple systems have been studied. Key words. binaries: eclipsing – : fundamental parameters – stars: individual: 65 UMa – stars: early-type

1. Introduction for studies of dynamical effects, the short and long-term evolu- tion of the orbits, etc. (see e.g. Söderhjelm 1975). As members of more complex multiple systems, the eclipsing The study of systems of higher multiplicity is still relatively binaries can provide us important information about their phys- undeveloped yet, and can provide insight into their formation. ical properties, as derived from different methods. This is the Moreover, Goodwin & Kroupa (2005) found that the major- case for 65 UMa, a system whose the close components form an ity of the early-type stars are found in multiple systems. - eclipsing binary, and additional components found to be grav- forming theories are still based on many ad hoc assumptions and itationally bounded to this pair (Pourbaix et al. 2004). Thanks the physical characteristics of the multiple systems can provide to the combined analysis, we have been able to derive the radii, strong constraints on some of them. These can be e.g. the mass masses, and evolutionary statuses of the close components, in ratios of the inner and outer pairs, the ratio of periods, and incli- addition to some properties of the distant ones. These systems nations, see for instance (Goodwin et al. 2007; Tokovinin 2008). are still very rare and mostly lie relatively close to the solar sys- In addition, the multiplicity fraction is one of the most crucial tem. Only 39 such systems are known where a close eclipsing parameters in theoretical models and nowadays we know of only binary is a member of a wide visual binary and we know both or- 20 quintuples, 11 sextuples, and 2 septuple systems (Eggleton & bits, their mutual inclinations, ratio of periods, etc. For instance, Tokovinin 2008). the ratio of periods can tell us something about the long-term sta- bility of the system. These unique systems are the most suitable 2. The system 65 UMa = + Reduced photometric and spectroscopic data, and Tables A.1–A.4 The multiple system 65 UMa ( WDS J11551 4629) consists of four visible components. The angular distance between the are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via primary and component D (=HR 4561) is about 63 , while the http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/542/A78 C component is at a distance of about 4. The primary 65 UMa Article published by EDP Sciences A78, page 1 of 6 A&A 542, A78 (2012)

AB = DN UMa, the brightest member of the system, was also re- Table 1. Parameters of the visual (A-B) orbit. solved to be a binary via classical micrometric measurements by Aitken (1908). Since then, many precise interferometric obser- Parameter Aristidi et al. (1999) This work vations of this close pair were carried out. Moreover, the primary pA−B [yr] 136.538 ± 8.4 118.209 ± 0.690 component was discovered to be a variable (Gimenez & Quesada aA−B [mas] 225 ± 18 208.2 ± 9.7 1979). Later, Gimenez & Quesada (1982) found the star to be an AA−B [d] – 0.0428 ± 0.0023 eclipsing binary with the of about 1.7304 d. Its TA−B 2447140.9 ± 149.7 2447516.9 ± 126.8 Ω ± ± variability was not discovered earlier owing to its rather shallow A−B [deg] 169.7 4.6 92.1 4.2 ± ± eclipses of only about 0.09 mag. This is caused by the presence ωA−B [deg] 26.9 2.1 202.7 1.3 iA−B [deg] 39.7 ± 1.9 38.1 ± 2.4 of other components in the aperture and therefore a large frac- ± ± tion of the third light, which reduces the photometric amplitude eA−B 0.531 0.014 0.504 0.006 of the eclipses. The light curve (hereafter LC) analysis presented by Garcia & Gimenez (1986) was slightly indicative of an eccen- tric orbit. The radial velocity curve (hereafter RV) was analyzed wavelength region 626–676 nm. All of them were secured by Popper (1986). All of these studies found that the close binary between March 2010 and July 2011 and have a resolving consists of two very similar stars. power R ∼ 12 700. Their S/N values range typically between 100 The position angle between the A and B components slowly and 300. changes, therefore an orbit of this pair was derived most recently For all of the spectra, the wavelength calibration was done by Aristidi et al. (1999), who found a period of about 137 yr using a ThAr comparison spectra obtained before and after the and a semi-major axis about 225 mas. The position angle of stellar spectra itself. The data reduction was performed fol- the pair has changed since this last paper by about 40◦, hence lowing the standard procedures of the data reduction package 1 a new analysis is required. Moreover, the combined analysis of IRAF . The flatfields were taken in the beginning and end of the visual orbit together with the times-of-minima variation due each night and their means were used in the data reduction. to the movement on this orbit and the radial-velocity variations After then, the radial velocities were obtained with the program can reveal some of the other parameters of the orbit and also of SPEFO (Horn et al. 1996; Škoda 1996), using the zero point cor- both AB and C components. The more distant C and D com- rection by measuring the telluric lines. In total, 55 spectra were ponents also belong to this multiple system, but these show no obtained in this way. detectable mutual motion and can be assumed to be motionless. All available data used for the analysis, the photometry, The MSC catalog by Tokovinin (1997) gives their periods 11 kyr times of minima, spectroscopy, and the interferometric measure- and 591 kyr, respectively. ments are also listed (see the CDS tables). A distance to 65 UMa was derived from the Hipparcos data. Perryman et al. (1997) gives the value of distance d = 246 ± 108 pc, while the new reduction of van Leeuwen (2007) 4. Visual orbit and the period analysis presented the value d = 212±30 pc. The combined spectral type To begin with, we analyzed the visual orbit. The orbital motion of the AB pair was classified as A3Vn by Cowley et al. (1969), influences the apparent period of the inner eclipsing pair, hence while the spectrum of the D component is A2p (Slettebak 1963), the periodic variation in the times of minima are analyzed ac- and Joshi et al. (2010) carried out an analysis of this star. On the cording to the visual orbit parameters. other hand, the spectral classification of the C component has Since its discovery as a double, 35 observations of the never been performed. Therefore, the mass of the C component A-B pair have been obtained. These have been collected in is also poorly constrained and the only information about this the Washington Double Star Catalog (hereafter WDS2, Mason star that we have is a rough estimate of the magnitude difference et al. 2001). We analyzed the data, obtaining the parameters of (see below). the visual orbit presented in Table 1, and the final fit together with the data is given in Fig. 1. As one can see from Table 1, 3. Observations and data reduction the parameters differ significantly in some aspects. Besides the higher precision, the most significant difference is found for the In total, the target was observed on 82 nights: 29 nights for orientation of the orbit in space. It is obvious that the same photometry, and 53 nights for spectroscopy. The complete fit to the data can be obtained with different sets of parame- BVRI light curves of the eclipsing pair were obtained in 2010 ters when we only interchange the values of two parameters: at the private observatory of one of the authors (RU). However, (Ω,ω) → (Ω+180◦,ω+ 180◦). However, when dealing with owing to the relatively high brightness of the target, only a small astrometric data set only, one cannot distinguish between these 254-mm reflector of moderate focal length was used. This tele- two identical solutions. The only way to do so is to use also the scope was unable to separate the two 4 distant components, RV data, or the times-of-minima variation. + therefore the resultant LC was a composite AB C light curve. For the minimum-times observations, we have only a limited The CCD photometric observations were obtained in standard B, set of data points. If we consider the period of the A-B pair to V,andR filters according to the specification of Bessell (1990). be about 118 yr, we have data for only about one-quarter of the All of the observations used for the LC were obtained with the orbital period covered with minima times at the present day. Yet, same telescope and instrument setup, and the reduction was also we can try to carry out an analysis of these data, by fixing the identical. Furthermore, the complete set of minima times used orbital parameters from (these in Table 1). We have for the analysis is given in Tables A.1–A.4 (available at the CDS), two new minima were measured by Petr Svoboda, Czech 1 IRAF is distributed by the National Optical Astronomy Republic. Observatories, which are operated by the Association of Universities The CCD spectra were obtained at Ondrejovˇ observatory, for Research in Astronomy, Inc., under cooperative agreement with the Czech Republic, using the 2.0-m telescope equipped with a National Science Foundation. SITe-005 800 × 2000 CCD detector. These spectra cover a 2 http://ad.usno.navy.mil/wds/

A78, page 2 of 6 P. Zasche et al.: Unique sextuple system: 65 UMa

2454000 2455000 2456000 0.01 E 0.015 2005 2006 2007 2008 2009 2010 2011 2012 0.1 1981 0.01 0.005

(days) 0.005

0.05 A−B N 1993 0 0 −0.005 O−C (Period) 0 −0.005 −0.01 (O−C)−(O−C) −0.015 −0.05 −0.01 1964 600 800 1000 1200 1400 1600 1800 2000 −0.1 Fig. 3. Period variation in the times of minima after subtraction of the DE [arcsec] −0.15 2007 118 yr term. Only the variation caused by the component Ab and the most recent minima have been displayed.

−0.2 Table 2. Final parameters of the short (Aa-Ab) orbit. −0.25 1908 Parameter Value −0.3 pAa−Ab [d] 641.5 ± 16.7 AAa−Ab [d] 0.00621 ± 0.00147 −0.35 TAa−Ab 24 49615.4 ± 38.9 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 ± RA [arcsec] ωAa−Ab [deg] 0.0 15.2 eAa−Ab 0.169 ± 0.048 Fig. 1. Visual orbit of 65 UMa pair (A-B) as displayed on the sky. The eclipsing binary is placed in [0, 0]. The dotted line represents the line of the apsides, while the dashed one is the line of the nodes. See Sect. 4. 640 day hypothesis. However, using the weightening scheme for the data points, the LITE fit based on the 640 day hypothesis 2444000 2446000 2448000 2450000 2452000 2454000 2456000 0.04 gives the sum of square residuals 0.00318, while disregarding 1980 1985 1990 1995 2000 2005 2010 0.02 the possibility of a 640 day period the sum is 0.01222. 0.02 0.01 Using the approach of combining the two LITE terms, one

0 0 can also derive the parallax of the system independently of the Hipparcos value and the total mass of the system. The method −0.02 −0.01 ⇒ ⇒ O−C (days) is as follows: (A − , a − ) π M . To briefly describe the

O−C (Period) A B A B tot −0.02 −0.04 method, the amplitude of LITE and the angular semi-major axis −0.03 of the visual orbit are directly connected via the parallax (Mayer −0.06 −5000 −4000 −3000 −2000 −1000 0 1000 2000 1990). Using our new computed parallax and the Kepler’s third Epoch law, we calculated the total mass of the system (e.g. Hilditch Fig. 2. Period variations of the eclipsing pair. Primary minima have been 2001). The values presented in Table 2 and the LITE semi- plotted as dots, and secondary as circles. The dashed line represents the amplitude AA−B were calculated using this approach. This means 118 yr orbit, while the solid one is the 640 day orbit. that the values of pA−B, TA−B, ΩA−B,ωA−B, iA−B,andeA−B were fixed, but the parameters AA−B, pAa−Ab, AAa−Ab, TAa−Ab,ωAa−Ab, and eAa−Ab were fitted as free parameters. From this analysis, a new value of the parallax π = 4.28 ± 0.49 mas was ob- regularly observed the minima of this interesting target for the tained, which yields the distance d = 234 ± 29 pc. Such a value past four years to detect the period variation. of parallax is slightly lower than the Hipparcos value (πHip = This led to an interesting finding that there is also an ad- 4.72 ± 0.58 mas). Using this new value of the parallax, we than ditional variation. We therefore analyzed our data set (43 data computed the total mass of the system Mtot = 8.25 ± 1.85 M. points in total) assuming two periodic terms. We used the LIght- Aristidi et al. (1999) found that M = 9.1 ± 11.6 M. ff tot Time-E ect hypothesis (hereafter LITE, described e.g. by Irwin The relative motion of the component C around AB is very 1959). The results of our analysis can clearly be seen in Figs. 2 slow, but detectable. During more than 200 years of obser- and 3. The long-term periodic modulation (blue) is caused by the vations, over 60 measurements were obtained (see the WDS) 118 yr visual orbit, while the short-period one is the newly dis- that revealed a change in position angle of about 5◦.Weana- covered orbit, whose final parameters derived from our analysis lyzed these data, determining a period of longer than 14 000 yr. are given in Table 2. This variation is clearly visible especially in However, this result is very preliminary owing to the poor cov- the more precise recent data points after subtraction of the long- erage of only 1/64 of the orbital period. period term, see Fig. 3. Here we use the following labeling of the components: Aa1 and Aa2 for the eclipsing binary compo- nents, Ab for the 640 day orbit, and B for the 118 yr orbit (i.e. 5. Light and radial velocity curves following the WDS notation). Thanks to the high precision of our new observations, the hypothesis of a non-circular orbit for To analyze the LC and RV curves, we had to consider a precise 65 UMa eclipsing pair was ruled out. The complete list of times ephemeris of the eclipsing pair. These followed from the mini- of minima together with the original BVRI photometry are given mum times analysis and resulted in the elements for the primary in Tables A.1–A.4 (available at the CDS). There is a problem minima with some of the minima times, whose accuracy is not always given, hence we cannot perform a reliable chi-square test of the HJD = 2 455 651.4491(5) + 1.7304736(32) · E. (1)

A78, page 3 of 6 A&A 542, A78 (2012)

Table 3. Parameters from the korel analysis. 150

100 Parameter Value 50 qAa1−2 (=MAa2/MAa1) 0.995 ± 0.012 −1 ± KAa1 [km s ] 133.3 4.2 0 K [km s−1] 135.7 ± 4.2 Aa2 RV [km/s] −50 qAa−Ab (= MAb/MAa1+Aa2)0.69± 0.11 K [km s−1] 19.9 ± 2.7 Ab −100 qA−B (= MB/MA)0.42± 0.14 −1 KB [km s ]0.41± 0.30 −150 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Phase

However, the analysis was not straightforward because of the ad- 150 ditional components in the system. We assumed that the C com- ponent does not affect the spectra significantly, since its distance 100 is about 4 . The observing conditions and seeing were usually 50 better than 2 during most nights. Hence, four other components were found to be present in each of the spectra. We used the pro- 0

korel RV [km/s] gram (Hadrava 2004) to disentangle the spectra. −50 To perform the spectral disentangling, the orbital elements of both orbits were fixed. Hence, the most crucial for the anal- −100 ysis were the values of the mass ratios and amplitudes of the −150 radial velocity curves. The ephemerides of the close eclipsing −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 pair were also kept fixed because these are much more reliably Phase known from the minima-times analysis. Fig. 4. Radial velocity curves of the 65 UMa eclipsing pair. The upper The parameters pAa−Ab, TAa−Ab, ωAa−Ab, eAa−Ab, pA−B, TA−B, plot shows the original RVs before correction for the 640 day variation. ωA−B,andeA−B were fixed. The results of the other relevant pa- The bottom plot shows the RVs of the eclipsing pair after the correction. rameters using korel are listed in Table 3. Despite the results of the mass ratios not being very conclusive, we were able to make some preliminary estimations of the masses of the indi- 6.4 I vidual components, as described below in Sect. 6.Sincekorel 6.45 does not provide an error estimation, the errors in the individual R parameters given in Table 3 resulted from the following analy- 6.5 sis. Several solutions in korel were calculated, from which only those with χ2 value closer than 5% from our best solution were 6.55 V considered. The errors in the parameters were assumed to be the maximum difference between these different solutions. Magnitude 6.6 B The program korel enables us to obtain the RVs of the indi- 6.65 vidual components, which can be used for some further analysis. We used our knowledge of the ephemerides of the inner pair and 6.7 the orbital parameters of the third body (i.e. 640 day orbit), to 6.75 subtract the 640 day term from the RVs of the eclipsing pair. This −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 can be clearly seen in Fig. 4, where the upper plot represents the Phase original radial velocities, while the bottom plot represents the velocities after the subtraction of this term. We achieved signifi- Fig. 5. BVRI light curves of 65 UMa together with the final phoebe fit. cant improvement in the quality of the RVs, which could be used The light curve parameters are given in Table 4. to perform a combined LC and RV analysis. The LC and RV curves of the eclipsing pair were analyzed using the program phoebe (Prša & Zwitter 2005), which is based gitimate to ask why a spectral classification of an A3 star was on the Wilson-Devinney program (WD, Wilson & Devinney made for the eclipsing binary (Cowley et al. 1969). This is due to 1971). The derived quantities are given in Table 4, while the LC presence of the component Ab on a 640 day orbit, whose spec- has been plotted in Fig. 5. The values of synchronicity Fi for tral type is probably of A3 and its light dominates the spectra. both eclipsing components were not derived from the combined Moreover, Garcia & Gimenez (1986) speculated that the eclips- LC and RV analysis. These were calculated from the spectra, ing binary components might be of A8-9 spectral type. The large and used to compute the values v sin i yielding the Fi values. The value of the third light is also well-established owing to the three errors in Fi are the standard deviations in Fi measured for differ- components that are present in the photometric aperture (in our ent spectra and different lines. The limb darkening was approxi- notation, components Ab+B+C). mated using a linear cosine law, and the values of xi were inter- The component Ab dominates the spectrum. This body has polated from the tables given in van Hamme (1993). In Table 4, a well-defined orbit, hence its lines can also be plotted with the we used the labeling of the two eclipsing components 1 and 2 in 640 day period. On the other hand, Ab orbits around a barycenter the indices instead of Aa1 and Aa2 for a better clarity. with the eclipsing pair. We can also plot the residuals from the The primary temperature was fixed at value T1 = 8000 K, LC fit from the eclipsing pair (from the original RVs), which which agrees with both the A7 spectral type (Cox 2000)and should vary in anti-phase with respect to the Ab lines. This is the masses of the components (see Table 4). Therefore, it is le- showninFig.6, where we have plotted the 640 day fit to our

A78, page 4 of 6 P. Zasche et al.: Unique sextuple system: 65 UMa

65 UMa Table 4. Light curve parameters of 65 UMa eclipsing pair.

Visual, ≈ 591 kyr, 63 Parameter Value ∗ T1 [K] 8000 D Visual, ≈ 14 kyr, 3.4 T2 [K] 7948 ± 20 i [deg] 86.5 ± 0.2 C Visual orbit, 118 yr, 0.18 ∗ g1 = g2 1.00 ∗ B SB, 641 day, 11 mas A1 = A2 1.00 F1 0.423 ± 0.094 Ab EB, SB, 1.73 day, 0.2 mas F2 0.384 ± 0.077 Aa1 Aa2 L1 (B) [%] 10.7 ± 0.4 =DNUMa L2 (B)[%] 9.7± 0.3 L B ± 3 ( ) [%] 79.6 1.5 Fig. 7. Schematic structure of the whole system 65 UMa. L1 (V) [%] 10.7 ± 0.5 L2 (V)[%] 9.8± 0.5 L3 (V) [%] 79.5 ± 2.1 L1 (R) [%] 10.7 ± 0.7 photometry, spectroscopy, and interferometry, obtaining quite a L2 (R)[%] 9.9± 0.7 reliable picture of this unusual sextuple hierarchical system (see ± L3 (R) [%] 79.5 3.3 Fig. 7). ± L1 (I) [%] 10.6 0.4 The inner close eclipsing pair consists of two almost- L2 (I)[%] 9.9± 0.4 ± identical stars of A7 spectral type. This finding is consistent L3 (I) [%] 79.5 1.8 with the photometric indices B − V, V − R,andR − I being Derived quantities: constant for the whole phase of the eclipsing binary at a level R [R]1.86± 0.08 1 of 0.005 mag. The stars move on circular orbits with periods R2 [R]1.81± 0.08 M1 [M]1.74± 0.06 of about 1.73043 d, both being located on the . M2 [M]1.71± 0.06 Thanks to the combined analysis, we were also able to com- pute its distance as d = 234 ± 29 pc, independently of the Notes. (∗) Fixed. Hipparcos satellite data. The 640 day orbit was confirmed by both the minima times and the RV variations. Applying the spec- 30 tral disentangling and rough estimation of the mass ratios from

20 this analysis, one can estimate the masses of the outer compo- nents. The Ab component is probably of A1 spectral type and 10 has a mass of about 2.4 ± 0.4 M, from the total mass of the

0 118 yr visual orbit, we can estimate the mass of the fourth com- ponent (in WDS named B), to be about 2.4 ± 2.0 M.Ifwe −10

RV [km/s] assume both these masses of Ab and B components, we can es- ff −20 timate the magnitude di erence. Aristidi et al. (1999) found this value to be 1.9 ± 0.1 mag, while here we derive 0.7 ± 4.5 mag. −30 The very large error is due to the large uncertainty in the mass

−40 of the fourth body. Another approach is to use the standard 55200 55300 55400 55500 55600 55700 55800 mass-luminosity relation and derive the individual luminosities Time (HJD−2400000) of the components. Using this approach, we have plotted Fig. 8, Fig. 6. Radial velocity curves on the 640 day orbit. The black squares where all components of the system 65 UMa are placed in the stand for the Ab lines in the spectrum, while the red circles represent the color–magnitude diagram. As one can see, the two eclipsing radial velocity residuals after subtraction of the eclipsing pair RV curve binaries are slightly under-luminous, while the D component (filled for primary, open for secondary). seems to be over-luminous. The same finding about its higher lu- minosity was found elsewhere, e.g. Joshi et al. (2010)orAurière spectra, which were acquired over two consecutive seasons 2010 et al. (2007). and 2011. However, some properties of the Aa-Ab orbit remain un- Moreover, during the photometric monitoring of 65 UMa, clear, such as the inclination angle between the orbits. We can two new variables were identified in the field. One of them do some rough estimation of this quantity. The korel KAa value was HD 103795 (spectrum K2III, according to Upgren 1962), and the predicted amplitude of radial-velocity variations from while the other one was SAO 43913 (spectrum F0, according the LITEAa−Ab are connected via sin iAa−Ab. Hence, we obtain ◦ to Slettebak & Stock 1959). Neither was ever reported to be a iAa−Ab ≈ 47 , which lies well between the inclinations i of the variable, despite both having been observed by the Hipparcos eclipsing pair and the iA−B of the visual orbit. Nevertheless, its satellite. However, our CCD photometry indicates that both are error is large but this is still only an estimation. We can also probably variable with amplitudes a few hundreds of magni- compute the predicted minimal angular separation of the Aa-Ab tude. SAO 43913 is probably a pulsating star (maybe δ Sct) pair for a prospective interferometric detection. This resulted in with a period of about three hours, but the type of variability about 11 mas, which is very favorable for modern stellar interfer- of HD 103795 remains unclear. ometers, because the magnitude difference between the Aa and Ab components should also be rather low. On the other hand, the 6. Discussion and conclusions angular separation of the eclipsing pair components is still rather low, at about only 0.18 mas. We have performed our first attempt to perform a detailed Dealing with a multiple system, we should also consider the combined solution of all available data for 65 UMa, namely nodal period of the close pair and the 640 day orbit, hence the

A78, page 5 of 6 A&A 542, A78 (2012)

−3 Aitken, R. G., & Moore, C. E. 1937, LicOB, 18, 53 −2 Aristidi, É., Prieur, J.-L., Scardia, M., et al. 1999, A&AS, 134, 545 Aurière, M., Wade, G. A., Silvester, J., et al. 2007, A&A, 475, 1053 −1 Bessell, M. S. 1990, PASP, 102, 1181 0 Brát, L., Trnka, J., Smelcer, L., et al. 2011, OEJV, 137, 1 Bulut, I., & Demircan, O. 2003, IBVS, 5476, 1

V 1 Cowley, A., Cowley, C., Jaschek, M., & Jaschek, C. 1969, AJ, 74, 375 2 Cox, A. N. 2000, in Allen’s Astrophysical Quantities, 4th edn., ed. A. N. Cox (New York: Springer Verlag) 3 Delgado-Donate, E. J., Clarke, C. J., & Bate, M. R. 2003, MNRAS, 342, 926 Magnitude M 4 Drózdz, M. 1997, International Amateur-Professional Photoelectric Photometry Hipparcos data Communications, 67, 30 5 Component Aa1 Component Aa2 Eggleton, P. P., & Tokovinin, A. A. 2008, MNRAS, 389, 869 6 Component Ab Garcia, J. M., & Gimenez, A. 1986, Ap&SS, 125, 181 Component B Gimenez, A., & Quesada, J. A. 1979, IBVS, 1648, 1 7 Component C Component D Gimenez, A., & Quesada, J. A. 1982, IBVS, 2068, 1 8 Goodwin, S. P., & Kroupa, P. 2005, A&A, 439, 565 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 Color index B−V Goodwin, S. P., Kroupa, P., Goodman, A., & Burkert, A. 2007, in Protostars and Planets V, ed. B. Reipurth, D. Jewitt, & K. Keil (Tucson: University of Fig. 8. Color–magnitude diagram for all components of the system. Arizona Press), 951, 133 Their position is compared with the Hipparcos stars (small black dots). Hadrava, P. 2004, PAICz, 92, 15 Hartkopf, W. I., & Mason, B. D. 2009, AJ, 138, 813 Hartkopf, W. I., McAlister, H. A., & Franz, O. G. 1992, AJ, 104, 810 change in the inclination of the eclipsing binary (Söderhjelm Hartkopf, W. I., McAlister, H. A., Mason, B. D., et al. 1994, AJ, 108, 2299 2 Hilditch, R. W. 2001, in An Introduction to Close Binary Stars, ed. R. W. Hilditch 1975). The most crucial here is the ratio of periods pAa−Ab /P, (Cambridge, UK: Cambridge University Press), 392 which implies that the nodal period was about 650 years, a du- Horn, J., Kubát, J., Harmanec, et al. 1996, A&A, 309, 521 ration that should be practical to observe. Unfortunately, we do Irwin, J. B. 1959, AJ, 64, 149 not have a complete set of orbital parameters of the Aa-Ab pair, Joshi, S., Ryabchikova, T., Kochukhov, O., et al. 2010, MNRAS, 401, 1299 so this is only first rough estimation. However, this nodal period Krajci, T. 2006, IBVS, 5690, 1 is not too long and potentially detectable. Further observations Krajci, T. 2007, IBVS, 5806, 1 Kuiper, G. P. 1961, ApJS, 6, 1 would help us to detect the change in the eclipse depths. Despite Lampens, P., Kleidis, S., van Cauteren, P., et al. 2010, IBVS, 5933, 1 these being rather shallow, this effect was detected in only nine Mason, B. D., Wycoff, G. L., Hartkopf, W. I., Douglass, G. G., & Worley, C. E. other cases, hence it would be interesting to reattempt detections, 2001, AJ, 122, 3466 especially with the modern ultra-precise satellite photometry. Mayer, P. 1990, BAICz, 41, 231 McAlister, H. A., Hartkopf, W. I., Gaston, B. J., Hendry, E. M., & Fekel, F. C. Nevertheless, 65 UMa is a rather unusual system, we 1984, ApJS, 54, 251 presently know of only 11 other sextuple systems (see Eggleton McAlister, H. A., Hartkopf, W. I., Hutter, D. J., & Franz, O. G. 1987, AJ, 93, 688 & Tokovinin 2008). The mass ratio of close to unity for the inner McAlister, H. A., Hartkopf, W. I., Sowell, J. R., Dombrowski, E. G., & Franz, pair seems to agree with some theoretical models of star forma- O. G. 1989, AJ, 97, 510 tion, e.g. Delgado-Donate et al. (2003). Moreover, some studies McAlister, H., Hartkopf, W. I., & Franz, O. G. 1990, AJ, 99, 965 McAlister, H. A., Mason, B. D., Hartkopf, W. I., & Shara, M. M. 1993, AJ, 106, (e.g. Tokovinin & Smekhov 2002) indicate that about one-third 1639 of all multiples are higher-order systems. Goodwin et al. (2007) Fu, H.-H., Hartkopf, W. I., Mason, B. D., et al. 1997, AJ, 114, 1623 discussed a finding that there is a difference between the num- Nagai K. 2006, Var. Star Bull., 44, 1 ber of observed and expected higher-order multiples (quadruples Perryman, M. A. C., Lindegren, L., Kovalevsky, J., et al. 1997, A&A, 323, L49 Popper, D. M. 1986, PASP, 98, 1312 and higher). Perhaps the discovery of other systems similar to Pourbaix, D., Tokovinin, A. A., Batten, A. H., et al. 2004, A&A, 424, 727 65 UMa would diminish this discrepancy. Prieur, J.-L., Oblak, E., Lampens, P., et al. 2001, A&A, 367, 865 Prša, A., & Zwitter, T. 2005, ApJ, 628, 426 Acknowledgements. Dr. Pavel Mayer is acknowledged for a useful discussion Slettebak, A. 1963, ApJ, 138, 118 and valuable advices. We would like to thank Mr. P. Chadima for obtain- Slettebak, A., & Stock, J. 1959, AAHam, 5, 105 ing the two spectra of 65 UMa at Ondrejovˇ observatory and P. Svoboda for Söderhjelm, S. 1975, A&A, 42, 229 sending us his photometric data for 65 UMa. This work was supported by Škoda, P. 1996, in Astronomical Data Analysis Software and Systems V, ed. the Czech Science Foundation grant No. P209/10/0715, by the research pro- G. H. Jacoby, & J. Barnes (San Fransicso: ASP), ASP Conf. Ser., 101, 187 gramme MSM0021620860 of the Czech Ministry of Education, and by the grant Tokovinin, A. A. 1997, A&AS, 124, 75 UNCE 12 of the Charles University in Prague. This research has made use of Tokovinin, A. 2008, MNRAS, 389, 925 the Washington Double Star Catalog maintained at the US Naval Observatory, Tokovinin, A. A., & Smekhov, M. G. 2002, A&A, 382, 118 the SIMBAD database, operated at CDS, Strasbourg, France, and of NASA’s Upgren, A. R. 1962, AJ, 67, 37 Astrophysics Data System Bibliographic Services. Van Biesbroeck, G. 1954, PYerO, 8, 6 van den Bos, W. H. 1960, PYerO, 9, 1 References van den Bos, W. H. 1962, AJ, 67, 555 van Hamme, W. 1993, AJ, 106, 2096 Aitken, R. G. 1908, LicOB, 5, 28 van Leeuwen, F. 2007, A&A, 474, 653 Aitken, R. G., & Doolittle, E. 1932, in New general catalogue of double stars Wilson, R. E., & Devinney, E. J. 1971, ApJ, 166, 605 within 120 of the North pole (Washington, D.C.: Carnegie institution of Worley, C. E. 1971, PUSNO, 22, 1 Washington Publications) Zasche, P., Wolf, M., Hartkopf, W. I., et al. 2009, AJ, 138, 664

A78, page 6 of 6